Abstract
Accurate temperature regulation is essential for ensuring product quality, operational safety, and energy efficiency in industrial electric furnace systems. However, the inherent thermal inertia, time-delay effects, and nonlinear dynamics of furnace processes often make precise temperature control a challenging task. Motivated by these challenges, this study proposes an optimization-based control framework aimed at improving the temperature regulation performance of electric furnace systems. The proposed approach integrates a proportional-integral-derivative (PID) controller with the recently developed gazelle optimization algorithm (GOA) for automatic tuning of the controller parameters. First, a mathematical model of the electric furnace is established to describe the dynamic relationship between the control input and the furnace temperature output. Based on this model, a PID controller is implemented to regulate the furnace temperature. The parameters of the PID controller are then optimized using GOA, a nature-inspired metaheuristic algorithm that mimics the adaptive predator-prey survival strategies observed in gazelle herds. In order to achieve a balanced improvement in both steady-state and transient performance, a composite objective function is introduced. The proposed performance index combines the integral of absolute error with additional transient performance indicators related to maximum overshoot and settling time. The effectiveness of the proposed GOA-based tuning framework is evaluated through extensive simulation studies and statistical analyses conducted over multiple independent optimization runs. The results demonstrate stable convergence behavior, with the optimization process achieving a minimum objective value of 2.4251, a maximum value of 2.5347, and an average value of 2.4674 across 25 runs. The optimized control system exhibits improved dynamic characteristics, including a rise time of 1.8509 s, a settling time of 3.6834 s, and a low overshoot of 1.5104%. To further assess its effectiveness, the proposed GOA-PID control strategy is compared with several widely used controller tuning methods reported in the literature, including genetic algorithm, Ziegler-Nichols, Cohen-Coon, Nelder-Mead, and direct synthesis approaches. Comparative results indicate that the proposed method achieves a superior balance between response speed, stability, and temperature tracking accuracy.